The Legislature — and Speaker Sheldon Silver’s Assembly, in particular — has one more week to raise the cap on charter schools and enact other education reforms in order to qualify for up to $700 million in federal school funding.

The deadline to apply for the cash, part of President Obama’s Race to the Top competition, is June 1 — though with the three-day state Democratic convention starting tomorrow (and Memorial Day weekend immediately thereafter), a deal really needs to be worked out today.

What’s at stake?

* There’s the $700 million, of course, which would be helpful in warding off the deepest of school-budget cuts — and which Silver can’t be looking forward to explaining away if New York loses out.

* And, since Albany can hardly be trusted to do the right thing for its own sake, it’s also the state’s last real chance for meaningful school reform.

Seriously: Would Silver even be thinking about allowing more charter schools if the man in the Oval Office wasn’t holding his feet to the fire?

The Senate did its part last month, passing a bill that would more than double the number of charters allowed statewide, to 460 from 200.

New York is on pace to hit the current cap this year, with demand for new seats at an all-time high.

After all, charters, which generally operate free of suffocating union work rules and bad-teacher protections, have been running circles around their unionized counterparts in student performance.

The wrangling in Albany, meanwhile, has been following a predictable pattern.

The teachers unions that pull Silver’s strings in the normal course of events can’t dispute charters’ success directly, so they’ve been laboring to slip poison pills into the cap-raiser bill that would, in effect, keep the schools in their place.

One would starve charters for space by barring them from sharing space with half-empty traditional schools.

This is particularly pernicious, given that charter schools get no public money for capital costs — and thus can’t build their own facilities.

For-profit charter schools, of which New York has but a handful, can borrow for new construction — which probably explains why the Assembly wants them dead, too.

Another poison pill would cap the number of charters per neighborhood, barring further parent choice in places like Harlem.

Finally, Silver would especially like to see SUNY stripped of its power to authorize charters, leaving that job solely to the Board of Regents, which he pretty much controls through Regents Chancellor Merryl Tisch.

Not that New Yorkers — or the White House — are likely to fall for it.